Abdelkarim Kari
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Best proximity point theorems for $ \alpha^{+} F, (\theta-\phi )$-proximal contraction Mohamed Rossafi; Abdelkarim Kari
Jurnal Matematika, Statistika dan Komputasi Vol. 18 No. 2 (2022): JANUARY 2022
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v18i2.17994

Abstract

In this paper, inspired by the idea of Suzuki type $ \alpha^{+} F$-proximal contraction in metric spaces, we prove a new existence of best proximity point for Suzuki type $ \alpha^{+} F$-proximal contraction and $ \alpha^{+} (\theta-\phi )$-proximal contraction defined on a closed subset of a complete metric space. Our theorems extend, generalize, and improve many existing results.
Fixed point theorem for Nonlinear $\theta-\phi-$contraction via $w-$distance Mohamed Rossafi; Abdelkarim Kari
Jurnal Matematika, Statistika dan Komputasi Vol. 19 No. 1 (2022): SEPTEMBER, 2022
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v19i1.20866

Abstract

This paper is aimed to the notion of $\theta-\phi-$contraction defined on a metric space with $w-$distance. Moreover, fixed point theorems are given in this framework. Some illustrative examples are provided to advocate the usability of our results.As an application, we prove the existence and uniqueness of a solution for the nonlinear Fredholm integral equations.
Generalized rational $ \alpha_{\ast}- $ contraction in $ C^{\ast}- $algebra-valued b-metric spaces Mohamed Rossafi; Hafida Massit; Abdelkarim Kari
Jurnal Matematika, Statistika dan Komputasi Vol. 19 No. 1 (2022): SEPTEMBER, 2022
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v19i1.21301

Abstract

This present paper extends some common fixed point theorems for generalized rational $ \alpha_{\ast}- $ contraction of multi-valued mappings in the setting of $ C^{\ast}- $algebra-valued b-metric spaces .