Abstract
Coincidence and common fixed point theorems for \(\beta\)-quasi contractive mappings on metric spaces endowed with binary relations and involving suitable comparison functions are presented. Our results generalize, improve, and extend several recent results. As an application, we study the existence of solutions for some class of integral equations.
Highlights
IntroductionThe Banach contraction principle [1] may be considered as one of most powerful tools for establishing existence and uniqueness of solutions for various non linear problems
The Banach contraction principle [1] may be considered as one of most powerful tools for establishing existence and uniqueness of solutions for various non linear problems.This principle is often used in the analysis of nonlinear governing equations arising in physics, engineering, economy and other disciplines
Coincidence and common fixed point theorems for b-quasi contractive mappings on metric spaces endowed with binary relations and involving suitable comparison functions are presented
Summary
The Banach contraction principle [1] may be considered as one of most powerful tools for establishing existence and uniqueness of solutions for various non linear problems. In order to prove Theorem 2.2, we will first need the following two lemmas: Lemma 3.6 In addition to the hypotheses of Theorem 2.2, suppose that xÃ; yà 2 Cðg; TÞ, gxà 1⁄4 gyÃ: Proof As C(g, T) is R-g-directed, there exists x0 2 X such that gxÃRgx0 and gyÃRgx0. Proof The coincidence point result follows immediately from Theorem 2.1 by taking a binary relation R given by x; y 2 X : xRy () x y: Corollary 4.3 Let (X, d) be a complete metric space endowed with a partial order such that ðX; d; Þ is regular. X be two commuting mappings such that g(X) is closed and TðXÞ & gðXÞ: Suppose there exists q 2 ð0; 1Þ satisfying dðTx; TyÞ q maxfdðgx; gyÞ; dðgx; TxÞ; dðgy; TyÞ; dðgx; TyÞ; dðgy; TxÞg; Proof It is an immediate consequence of the previous corollary where uðtÞ 1⁄4 qt. We will apply Theorem 2.1 to establish some conditions which guarantee the existence of solutions for some generalized
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
