Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Existence of Common Fixed Points of Generalized ∆-Implicit Locally Contractive Mappings on Closed Ball in Multiplicative G-metric Spaces with Applications

Version 1 : Received: 11 September 2022 / Approved: 13 September 2022 / Online: 13 September 2022 (04:44:36 CEST)

A peer-reviewed article of this Preprint also exists.

Rasham, T.; Nazam, M.; Aydi, H.; Agarwal, R.P. Existence of Common Fixed Points of Generalized Δ-Implicit Locally Contractive Mappings on Closed Ball in Multiplicative G-Metric Spaces with Applications. Mathematics 2022, 10, 3369. Rasham, T.; Nazam, M.; Aydi, H.; Agarwal, R.P. Existence of Common Fixed Points of Generalized Δ-Implicit Locally Contractive Mappings on Closed Ball in Multiplicative G-Metric Spaces with Applications. Mathematics 2022, 10, 3369.

Abstract

In this paper, we introduced a generalized ∆-implicit locally contractive condition and give some examples to support it and to show its significance in fixed point theory. We prove that the mappings satisfying generalized ∆-implicit locally contractive condition admits a common fixed point, where, the ordered multiplicative GM−metric space is chosen as underlying space. The obtained fixed point theorems generalize many earlier fixed point theorems on implicit locally contractive mappings. In addition, some nontrivial and interesting examples are provided to support our findings. To demonstrate the originality of our new main result, we apply it to show existence of solutions to a system of nonlinear -Volterra type- integral equations.

Keywords

ordered complete multiplicative GM−metric space; closed ball; integral equations; locally generalized ∆-implicit contraction

Subject

Computer Science and Mathematics, Mathematics

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