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Fixed-Point Theorems in Generalized Modular Metric Spaces

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Metric Fixed Point Theory

Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

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Abstract

Modular function spaces are one of the unique conditions of modular vector spaces which were defined by Nakano [37] in 1950. Later on, Khamsi, Kozlowski, and Reich [28] introduced the fixed-point principle in modular function spaces in 1990. Chistyakov introduced concept of a modular metric space in 2011 [14]. Abdou and Khamsi introduced fixed-point theory into the modular metric spaces using different techniques from the viewpoint of Chistyakov [14, 15], the similar approach continues in this part as they used in [1]. In this chapter, the Banach Contraction Principle and Ćirić Quasi-contraction are proven in Generalized Modular Metric Spaces (briefly GMMS). The usual topology is defined on these spaces, and then, using Nadler [36] and Edelstein’s results in [1], two fixed-point theorems are given for a multivalued contractive-type map in the construction of modular metric spaces. They are Caristi and Feng-Liu types in GMMS with their applications as in [42] and [43].

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts & Sciences, Erzincan University, Erzincan, Turkey

    N. Manav

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  1. N. Manav
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Correspondence to N. Manav .

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Editors and Affiliations

  1. Department of Applied Science and Humanities, Assam University, Silchar, India

    Pradip Debnath

  2. Department of Mathematics, Birjhora Mahavidyalaya, Bongaigaon, India

    Nabanita Konwar

  3. Faculty of Mechanical Engineering, University of Belgrade, Belgrade, Serbia

    Stojan Radenović

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Manav, N. (2021). Fixed-Point Theorems in Generalized Modular Metric Spaces. In: Debnath, P., Konwar, N., Radenović, S. (eds) Metric Fixed Point Theory. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-16-4896-0_5

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