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Set-valued $$(\Psi ,\Phi )$$ ( Ψ , Φ ) - $$\Theta $$ Θ ordered contractions with applications in differential inclusions

Set-valued $$(\Psi ,\Phi )$$ ( Ψ , Φ ) - $$\Theta $$ Θ ordered contractions with applications in... J Anal https://doi.org/10.1007/s41478-018-0107-4 ORIGINAL RESEARCH PAPER Set‑valued (𝚿 , 𝚽) ‑  ordered contractions with applications in differential inclusions 1 2 2 Akbar Azam  · Maliha Rashid  · Nayyar Mehmood Received: 18 February 2018 / Accepted: 2 June 2018 © Forum D’Analystes, Chennai 2018 Abstract In this article we prove some results for coincidence points of a new type of set-valued (Ψ, Φ)-Θ contractions in the settings of ordered metric spaces. Our results generalize many results in the literature. We also provide some nontrivial examples to support our main theorem. For application of our main result, we pro- vide an existence theorem for solutions of hyperbolic type differential inclusions. Keywords Ordered metric space · Multi-valued mappings · Multivalued (Ψ, Φ)-Θ contraction · Coincidence points · Differential inclusions Mathematics Subject Classification Primary 47H10 · 54H25 1 Introduction The order-theoretic fixed point theory has its applications to a wide range of various fields such as, e.g., (single and multi-valued) non-local discontinuous partial differ - ential equations of various types, ordinary differential equations (inclusions), inte - gral equations (inclusions), mathematical economics and game theory. In all these This paper is in final form and no version of it will be submitted for publication elsewhere. * Nayyar Mehmood nayyarmaths@gmail.com Akbar Azam akbarazam@yahoo.com Maliha http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

Set-valued $$(\Psi ,\Phi )$$ ( Ψ , Φ ) - $$\Theta $$ Θ ordered contractions with applications in differential inclusions

The Journal of Analysis , Volume OnlineFirst – Jun 11, 2018

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Forum D'Analystes, Chennai
Subject
Mathematics; Analysis; Functional Analysis; Abstract Harmonic Analysis; Special Functions; Fourier Analysis; Measure and Integration
ISSN
0971-3611
eISSN
2367-2501
DOI
10.1007/s41478-018-0107-4
Publisher site
See Article on Publisher Site

Abstract

J Anal https://doi.org/10.1007/s41478-018-0107-4 ORIGINAL RESEARCH PAPER Set‑valued (𝚿 , 𝚽) ‑  ordered contractions with applications in differential inclusions 1 2 2 Akbar Azam  · Maliha Rashid  · Nayyar Mehmood Received: 18 February 2018 / Accepted: 2 June 2018 © Forum D’Analystes, Chennai 2018 Abstract In this article we prove some results for coincidence points of a new type of set-valued (Ψ, Φ)-Θ contractions in the settings of ordered metric spaces. Our results generalize many results in the literature. We also provide some nontrivial examples to support our main theorem. For application of our main result, we pro- vide an existence theorem for solutions of hyperbolic type differential inclusions. Keywords Ordered metric space · Multi-valued mappings · Multivalued (Ψ, Φ)-Θ contraction · Coincidence points · Differential inclusions Mathematics Subject Classification Primary 47H10 · 54H25 1 Introduction The order-theoretic fixed point theory has its applications to a wide range of various fields such as, e.g., (single and multi-valued) non-local discontinuous partial differ - ential equations of various types, ordinary differential equations (inclusions), inte - gral equations (inclusions), mathematical economics and game theory. In all these This paper is in final form and no version of it will be submitted for publication elsewhere. * Nayyar Mehmood nayyarmaths@gmail.com Akbar Azam akbarazam@yahoo.com Maliha

Journal

The Journal of AnalysisSpringer Journals

Published: Jun 11, 2018

References