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3. Hybrid Fractional Differential Equations

Author

Benchohra, Mouffak, Karapınar, Erdal, Lazreg, Jamal Eddine, Salim, Abdelkrim, Krantz, Steven G., Series Editor, Benchohra, Mouffak, Karapınar, Erdal, Lazreg, Jamal Eddine, and Salim, Abdelkrim

Published
2023
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7. Preliminary Background

Author

Benchohra, Mouffak, Karapınar, Erdal, Lazreg, Jamal Eddine, Salim, Abdelkrim, Krantz, Steven G., Series Editor, Benchohra, Mouffak, Karapınar, Erdal, Lazreg, Jamal Eddine, and Salim, Abdelkrim

Published
2023
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8. Introduction

Author

Benchohra, Mouffak, Karapınar, Erdal, Lazreg, Jamal Eddine, Salim, Abdelkrim, Krantz, Steven G., Series Editor, Benchohra, Mouffak, Karapınar, Erdal, Lazreg, Jamal Eddine, and Salim, Abdelkrim

Published
2023
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12. Fuzzy ample spectrum contractions in (more general than) non-Archimedean fuzzy metric spaces

Author

de Hierro, Antonio Francisco Roldán López, Karapınar, Erdal, and Shahzad, Naseer

Subjects
Mathematics - General Mathematics, 47H10, 47H09, 54H25, 46T99
Abstract

Taking into account that Rold\'an et al.'s ample spectrum contractions have managed to extend and unify more than ten distinct families of contractive mappings in the setting of metric spaces, in this manuscript we present a first study on how such concept can be implemented in the more general framework of fuzzy metric spaces in the sense of Kramosil and Mich\'alek. We introduce two distinct approaches to the concept of fuzzy ample spectrum contractions and we prove general results about existence and uniqueness of fixed points. The proposed notions enjoys the following advantages with respect to previous approaches: (1) they permit to develop fixed point theory in a very general fuzzy framework (for instance, the underlying fuzzy space is not necessarily complete); (2) the procedures that we employ are able to overcome the technical drawbacks raising in fuzzy metric spaces in the sense of Kramosil and Mich\'alek (that do not appear in fuzzy metric spaces in the sense of George and Veeramani); (3) we introduce a novel property about sequences that are not Cauchy in a fuzzy space in order to consider a more general context than non-Archimedean fuzzy metric spaces; (4) the contractivity condition associated to fuzzy ample spectrum contractions does not have to be expressed in separate variables; (5) such fuzzy contractions generalize some well-known families of fuzzy contractive operators such that the class of all Mihet's fuzzy $\psi$-contractions. As a consequence of these properties, this study gives a positive partial answer to a question posed by this author some years ago.

Published
2021

15. Metric Spaces

Author

Karapınar, Erdal, Agarwal, Ravi P., Krantz, Steven G., Series Editor, Karapinar, Erdal, and Agarwal, Ravi P.

Published
2022
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18. Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points

Author

Karapınar Erdal, Romaguera Salvador, and Tirado Pedro

Subjects
quasi-metric, complete, w-distance, fixed point, g-metric, 47h10, 54h25, 54e50, Mathematics, QA1-939
Abstract

Involving ww-distances we prove a fixed point theorem of Caristi-type in the realm of (non-necessarily T1{T}_{1}) quasi-metric spaces. With the help of this result, a characterization of quasi-metric completeness is obtained. Our approach allows us to retrieve several key examples occurring in various fields of mathematics and computer science and that are modeled as non-T1{T}_{1} quasi-metric spaces. As an application, we deduce a characterization of complete GG-metric spaces in terms of a weak version of Caristi’s theorem that involves a G-metric version of w-distances.

Published
2022
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20. Introduction

Author

Benchohra, Mouffak, primary, Karapınar, Erdal, additional, Lazreg, Jamal Eddine, additional, and Salim, Abdelkrim, additional

Published
2023
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21. Preliminary Background

Author

Benchohra, Mouffak, primary, Karapınar, Erdal, additional, Lazreg, Jamal Eddine, additional, and Salim, Abdelkrim, additional

Published
2023
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24. Perov-Type Contractions

Author

Cvetković, Marija, Karapınar, Erdal, Rakočević, Vladimir, Yeşilkaya, Seher Sultan, Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Daras, Nicholas J., editor, and Rassias, Themistocles M., editor

Published
2022
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26. A Survey on Interpolative and Hybrid Contractions

Author

Karapınar, Erdal, Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Parasidis, Ioannis N., editor, Providas, Efthimios, editor, and Rassias, Themistocles M., editor

Published
2021
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30. Dynamics and Ulam Stability for Fractional q-Difference Inclusions via Picard Operators Theory

Author

Abbas Saïd, Benchohra Mouffak, and Karapınar Erdal

Subjects
fractional q-difference inclusion, multivalued weakly picard operator, ulam-rassias stability, fixed point inclusion, primary 26a33, 34a60, secondary 46t99, 47h10, Mathematics, QA1-939
Abstract

In this manuscript, by using weakly Picard operators we investigate the Ulam type stability of fractional q-difference An illustrative example is given in the last section.

Published
2021
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31. Introduction

Author

Karapınar, Erdal, Agarwal, Ravi P., Krantz, Steven G., Series Editor, Karapinar, Erdal, and Agarwal, Ravi P.

Published
2022
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34. Perov-Type Contractions

Author

Cvetković, Marija, primary, Karapınar, Erdal, additional, Rakočević, Vladimir, additional, and Yeşilkaya, Seher Sultan, additional

Published
2022
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35. Impulsive Caputo-Fabrizio fractional differential equations in b-metric spaces

Author

Lazreg Jamal Eddine, Abbas Saïd, Benchohra Mouffak, and Karapınar Erdal

Subjects
fractional differential equation, caputo-fabrizio integral of fractional order, caputo-fabrizio fractional derivative, instantaneous impulse, b-metric space, α-ϕ-geraghty contraction, fixed point, 47h10, 54h25, Mathematics, QA1-939
Abstract

We deal with some impulsive Caputo-Fabrizio fractional differential equations in bb-metric spaces. We make use of α-ϕ\alpha \text{-}\phi -Geraghty-type contraction. An illustrative example is the subject of the last section.

Published
2021
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37. Some consequences of Caristi's fixed point theorem, partial answers to some known open problems and its applications

Author

Khojasteh, Farshid, Karapinar, Erdal, and Khandani, Hassan

Subjects
Mathematics - Metric Geometry, Mathematics - Functional Analysis
Abstract

In this paper, we show that several extension of Banach contraction principle, can be easily derived from the Caristi's theorem is one of the useful generalization of Banach contraction principle in the setting of the complete metric spaces. Moreover, some partial answers to some known open problems are given via Caristi's corollaries. Finally, existence of bounded solutions of a functional equation is studied to support our results.

Published
2015

38. Some applications of Caristi's fixed point theorem in metric space

Author

Khojasteh, Farshid, Karapinar, Erdal, and Khandani, Hasan

Subjects
Mathematics - Optimization and Control
Abstract

In this work, partial answers to Reich, Mizoguchi and Takahashi, and Amini-Harandi's conjectures are presented via a light version of Caristi's fixed point theorem. Moreover, we introduce that many of known fixed point theorem can easily derived from the Caristi's theorem. Finally, existence of bounded solutions of a functional equation is studied., Comment: arXiv admin note: substantial text overlap with arXiv:1506.05060

Published
2015

42. Abstract random differential equations with state-dependent delay using measures of noncompactness.

Author

Heris, Amel, Bouteffal, Zohra, Salim, Abdelkrim, Benchohra, Mouffak, and Karapınar, Erdal

Subjects
DIFFERENTIAL equations, EXISTENCE theorems, GENERALIZATION, FIXED point theory, FRECHET spaces
Abstract

This paper is devoted to the existence of random mild solutions for a general class of second-order abstract random differential equations with state-dependent delay. The technique used is a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measures of noncompactness. An application related to partial random differential equations with state-dependent delay is presented. [ABSTRACT FROM AUTHOR]

Published
2024
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48. Discussions on the almost 𝒵-contraction

Author

Karapınar Erdal and Hima Bindu V. M. L.

Subjects
almost k contraction, simulation function, almost contraction, α admissible, e contraction, 55m20, 54h25, 47h10, Mathematics, QA1-939
Abstract

In this paper, we introduce a new contraction, namely, almost Z{\mathcal{Z}} contraction with respect to ζ∈Z\zeta \in {\mathcal{Z}}, in the setting of complete metric spaces. We proved that such contraction possesses a fixed point and the given theorem covers several existing results in the literature. We consider an example to illustrate our result.

Published
2020
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