Research & Science Group Ltd.Communications in Nonlinear Analysis2371-792010120220701Some Inequalities for the Polar Derivative of a Polynomial Having S-Fold Zeros at the Origin17110884ENM HGulzarDepartment of Mathematics, University of Kashmir, Srinagar 190006, Jammu and Kashmir, IndiaBashir AhmadZargarDepartment of Mathematics, University of Kashmir, Srinagar 190006, Jammu and Kashmir, IndiaRubiaAkhterDepartment of Mathematics, University of Kashmir, Srinagar 190006, Jammu and Kashmir, IndiaJournal Article20200210Let $P(z)$ be a polynomial of degree $n$ having all its zeros in $|z|\leq 1$ then for all $(\alpha_i)^t_{i=1}\in \mathbb{C}$ with $|\alpha_i|\geq 1, 1\leq i\leq t<n$, it was proved by Jain[V. K. Jain, Generalization of an inequality involving maximum moduli of a polynomial and its polar derivative, Bull Math Soc Sci Math Roum Tome. 98, 67–74 (2007)] that<br />\begin{align*}<br />\max\limits_{|z|=1}|D_{\alpha_t}...D_{\alpha_2}D_{\alpha_1}P(z)|\geq\frac{n_t}{2^t}\left[A_{\alpha_t}\max\limits_{|z|=1}|P(z)|+\left( 2^t\prod\limits_{i=1}^{t}|\alpha_i|- A_{\alpha_t}\right)\min\limits_{|z|=1}|P(z)| \right].<br />\end{align*}<br />where $n_t=n(n-1)...(n-t+1)$ and $A_{\alpha_t}=(|\alpha_1|-1)(|\alpha_2|-1)...(|\alpha_t|-1)$. In this paper, we generalize this and some other results.https://www.cna-journal.com/article_110884_ca06be3627cafc370e24d8f0e3c1e717.pdfResearch & Science Group Ltd.Communications in Nonlinear Analysis2371-792010120220701Coincidence Points with φ-Contractions in Partially Ordered Fuzzy Metric Spaces113111011ENBinayak SChoudhuryDepartment of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B. Garden, Shibpur, Howrah -
711103, West Bengal, IndiaPradyutDasDepartment of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B. Garden, Shibpur, Howrah -
711103, West Bengal, IndiaParbatiSahaDepartment of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B. Garden, Shibpur, Howrah -
711103, West Bengal, IndiaSamir KumarBhandariDepartment of Mathematics, Bajkul Milani Mahavidyalaya, P.O-Kismat Bajkul, Purba Medinipur, Pin- 721655,
West-Bengal, IndiaJournal Article20200421In this paper our main result is a coupled coincidence point theorem for a compatible pair<br />in a fuzzy metric space with a partial ordering under the assumption of a new coupled contraction inequality which involves a recently introduced control function which is a generalization of<br />many such functions previously used in literatures. The proof depends on a lemma in which we<br />prove a condition for simultaneous holding of Cauchy criteria for two sequences. We use H-type<br />t-norms in this paper in order to utilize the equi-continuity of the t-norm iterates in the proof<br />of the lemma. The contraction inequality also involves another function which is borrowed from<br />a recent work, there is a partial ordering defined on the fuzzy metric space. There are several<br />corollaries of the main theorem. An illustrative example is given.https://www.cna-journal.com/article_111011_cbefbf3abaa81f1d49261649f5516925.pdfResearch & Science Group Ltd.Communications in Nonlinear Analysis2371-792010120220701Isolation Effect on Age-Stratified Compartmental Model of the COVID-19116129510ENM. D. ShahidulIslamDepartment of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh0000-0003-4712-4046K. M.Ariful KabirDepartment of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, BangladeshJannatunIrana IraDepartment of Mathematics, University of Dhaka, Dhaka 1000, BangladeshMahadeeAl MobinDepartment of Mathematics, University of Dhaka, Dhaka 1000, BangladeshMd. Haider AliBiswasMathematics Discipline, Khulna University, Khulna 9208, BangladeshPraveenKumar GuptaDepartment of Mathematics, National Institute of Technology, Silchar-788010, Assam, IndiaJournal Article20210228Focusing on the dynamics of the most recent outbreak of COVID-19, we formulate an age distributed model with five different components in terms of nonlinear partial differential equations. The model has been analyzed by studying the stability of the equilibrium points and their reproduction number. To explore the disease effect on different ages more efficiently, we apply the recent estimated data in the formulated model and analyze it numerically. From the model’s numerical solution profiles, we observed more susceptibility and infection among the older population. Also studied the effectiveness of isolation in controlling illness and death.https://www.cna-journal.com/article_129510_f32f72d216c9796e06b9ea48d9084249.pdfResearch & Science Group Ltd.Communications in Nonlinear Analysis2371-792010120220701On New Fixed Point Results for Some Classes of Enriched Mappings in N-Banach Spaces19132132ENEsraSimsekDepartment of Mathematics, Faculty of Science, Ataturk University, 25240 Erzurum, Turkey.IsaYildirimDepartment of Mathematics, Faculty of Science, Ataturk University, 25240 Erzurum, Turkey.0000-0001-6165-716XJournal Article20210429We introduce the concepts of enriched n-contraction mapping, enriched n-Chatterjea mapping and enriched n-Kannan mapping in linear n-normed space. We prove some fixed point theorems for such mappings using Krasnoselsij iteration process in n-Banach spaces. The results presented in this paper improve the recent works of Berinde and Pacurar (J. Fixed Point Theory Appl. (2020) 22-38), Berinde and Pacurar (Preprint, arXiv:1909.03494) and Berinde and Pacurar (Preprint, arXiv:1909.02379, 2019) to linear n-normed spaces.https://www.cna-journal.com/article_132132_6fa9553000068becb11d5c0330f1ae6f.pdfResearch & Science Group Ltd.Communications in Nonlinear Analysis2371-792010120220701Convergence Theorems for Monotone Generalized α-Nonexpansive Mappings in Ordered Banach Space by a New Four-Step Iteration Process With Application118133752ENUnwanaUdofiaDepartment of Mathematics and Statistics, Akwa Ibom state University, Ikot Akpaden, Mkpatenin, Nigeria0000-0002-8640-5804DonatusIgbokweDepartment of Mathematics,
Michael Okpara University of Agriculture,
Umudike, Abia State,
Nigeria.0000-0002-8574-6658Journal Article20210718We introduce a new four-step iterative algorithm and show that the new algorithm converges faster than a number of existing iterative algorithms for contraction mappings. We prove strong and weak convergence results for approximating fixed points of monotone generalized α-nonexpansive mappings. Further, we utilize our proposed algorithm to solve Split Feasibility Problem (SFP). Our result complements, extends and generalizes some existing results in literature.https://www.cna-journal.com/article_133752_4223a5c90758b1c9fc90e7d039ab5267.pdfResearch & Science Group Ltd.Communications in Nonlinear Analysis2371-792010120220701A Split Common Fixed Point and Null Point Problem for Lipschitzian Quasi Pseudocontractive Mappings in Hilbert Spaces114132133ENUko SundayJimDepartment of Mathematics, University of Uyo, Nigeria.Daonatus IkechiIgbokweDepartment of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State - NigeriaJournal Article20210504A split common fixed point and null point problem (SCFPNPP) which includes the split<br />common fixed point problem, the split common null point problem and other problems related to the fixed point<br />problem and the null point problem is studied. We introduce a Halpern--Ishikawa type algorithm for studying the split common fixed point and null point problem for Lipschitzian quasi pseudocontractive operators and maximal monotone operators in real Hilbert spaces. Moreover, we establish a strong convergence results under some suitable conditions and reduce our main result to above-mentioned problems. <br />We give numerical result to demonstrate the convergence of our algorithms and compare rate of convergence some iterative algorithms. Finally, we applied the study to split feasibility problem (FEP), split equilibrium problem (SEP), split variational inequality problem (SVIP) and split optimization problem (SOP).Research & Science Group Ltd.Communications in Nonlinear Analysis2371-792010120220701Approximating endpoints of multi-valued generalized $\alpha$-nonexpansive mappings in Banach spaces118118113ENJunaidAhmadDepartment of Mathematics, Uuniversity of Science and Technology,Bannu 28100, Khyber Pakhtunkhwa, PakistanKifayatUllahDepartment of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, PakistanMuhammad Safi UllahKhanDepartment of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, PakistanNaseerMuhammadDepartment of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, PakistanJournal Article20200429In this paper, we study endpoints of multi-valued generalized $\alpha$-nonexpansive mappings in Banach spaces. Under some appropriate assumptions, we prove that the sequence of modified Agarwal-O'Rega-Sahu iterative process defined by Abdeljawad et al. (2020) converges strongly to an endpoint of a multi-valued generalized $\alpha$-nonexpansive mappings. We also give an illustrate example. Our results are new and extend the corresponding results of the current literature.Research & Science Group Ltd.Communications in Nonlinear Analysis2371-792010120220701The Approximate Solution of COVID-19 Model by Variational Iteration Method118138226ENEiman.Department of Mathematics, University of Malakand, Chakdara Dir (Lower),
Khyber Pakhtunkhawa, Pakistan,HazratZamanUniversity of MalakandZakirUllahUniversity of MalakandJournal Article20210817In this work, we investigate a mathematical model of COVID-19 for approximate solution through variation iteration method (VIM). With the help of the said technique, we develop an algorithm to compute series type solution to the proposed problem. Then using some real values for the parameters and initial data, we compute few terms approximate solutions corresponding to different compartment. With the help of Mathematica, we also plot our approximate solutions for different compartment graphically.Research & Science Group Ltd.Communications in Nonlinear Analysis2371-792010120220701NONLINEAR COUPLED COINCIDENCE AND COUPLED FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN PARTIALLY ORDERED PROBABILISTIC METRIC SPACES120102593ENSAURABHMANRO223, block no.33 ,peer khana road near tewari kothiABDELKRIMABDELHALIM,Department of Mathematics and Informatics, Larbi Ben M'hidi University,
Oum El Bouaghi, Algeria.BEN AOUALEILA,Department of Mathematics and Informatic, The Larbi Ben M'hidi Univer-
sity, Oum El Bouaghi, Algeria.ABDELKRIM ALIOUCHE,ABDELKRIM ALIOUCHE,Department of Mathematics, The Larbi Ben M'hidi University, Oum El
Bouaghi, Algeria.OUSSAEIF TAKI-EDDINE,OUSSAEIF TAKI-EDDINE,Department of Mathematics and Informatics. The Larbi Ben M'hidi Univer-
sity, Oum El Bouaghi.Journal Article20191206In this paper, we introduce the notion of weaker compatibility<br />of mappings in partially ordered probabilistic metric spaces and use this no-<br />tion to establish a coupled coincidence point results. Very recently Dragan<br />Doric [Nonlinear coupled coincidence and coupled xed point theorems for not<br />necessary commutative contractive mappings in partially ordered probabilistic<br />spaces] proved coupled coincidence point theorems for compatible mappings<br />in partially ordered probabilistic metric spaces. In this paper we proved re-<br />sults of Dragam under a dierent set of conditions. Precisely, we establish<br />our results by assuming that two mappings in partially ordered probabilistic<br />metric spaces are weakly compatible. Our results improve and extend a cou-<br />pled xed point theorem due to Bhaskar and Lakshmikantham [T-G.Bhaskar ,<br />V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces<br />and applications, Nolinear Anal, 65(2006) 1379-1393]. An example is given to<br />support our result.In this paper, we introduce the notion of weaker compatibility<br />of mappings in partially ordered probabilistic metric spaces and use this no-<br />tion to establish a coupled coincidence point results. Very recently Dragan<br />Doric [Nonlinear coupled coincidence and coupled xed point theorems for not<br />necessary commutative contractive mappings in partially ordered probabilistic<br />spaces] proved coupled coincidence point theorems for compatible mappings<br />in partially ordered probabilistic metric spaces. In this paper we proved re-<br />sults of Dragam under a different set of conditions. Our results improve and extend a cou-<br />pled xed point theorem due to Bhaskar and Lakshmikantham. An example is given to<br />support our result.