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

Tahair Rasham, Muhammad Nazam, Hassen Aydi and Ravi P. Agarwal ()
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Tahair Rasham: Department of Mathematics, University of Poonch Rawalakot Azad Kashmir, Azad Kashmir 12350, Pakistan
Muhammad Nazam: Department of Mathematics, Allama Iqbal Open University, Islamabad 44000, Pakistan
Hassen Aydi: Institut Supérieur d’Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
Ravi P. Agarwal: Department of Mathematics, Texas A&M University-Kingsville, 700 University Blvd., MSC 172, Kingsville, TX 78363-8202, USA

Mathematics, 2022, vol. 10, issue 18, 1-17

Abstract: In this paper, we introduce a generalized Δ -implicit locally contractive condition and give some examples to support it and show its significance in fixed point theory. We prove that the mappings satisfying the generalized Δ -implicit locally contractive condition admit a common fixed point, where the ordered multiplicative G M -metric space is chosen as the 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 the existence of solutions to a system of nonlinear—Volterra type—integral equations.

Keywords: ordered complete multiplicative G M -metric space; closed ball; integral equations; locally generalized ?-implicit contraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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