Best proximity point (pair) theorem using ( α − ς ) Meir-Keeler condensing operators in Busemann convex spaces

• Pradhan, Akash ^[1] ; Gabeleh, Moosa ^[3] ; Patel, Deepesh Kumar ^[1] ; Samei, Mohammad Esmael ^[2]
  1. [1] Visvesvaraya National Institute of Technology

     Visvesvaraya National Institute of Technology

     India

     
  2. [2] Bu-Ali Sina University

     Bu-Ali Sina University

     Irán

     
  3. [3] Ayatollah Boroujerdi University

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 26, Nº. 2, 2025, págs. 763-784
• Idioma: inglés
• DOI: 10.4995/agt.2025.23065
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• Resumen

  • Two new class of condensing operators, called  ( α − ς ) and ( β − ς ) Meir-Keelercondensing operators, are introduced and used to investigate the existence of best proximity points (pairs) for cyclic (noncyclic) relatively nonexpansive mappings to more general metric space, namely reflexive and Busemann convex space by applying measure of noncompactness. In this way, we extend the main results of the paper [M. Gabeleh, C. Vetro, A new extension of Darbo's fixed point theorem using relatively Meir-Keeler condensing operators, Bull. Aust. Math. Soc., 98 (2022), 247-266] from Banach spaces to Busemann convex metric spaces and by considering appropriate control functions. Some related examples are also presented to describe these classes of operators. Finally, as an application of our main conclusions, we survey the existence of an optimal solution for a certain type of system of integro-differential equations.

• Referencias bibliográficas
  • A. Ambrosetti, Un teorema di esistenza per ie equazioni differenziali negli spazi di banach, Rend. Sem. Mat. Padova 39 (1967), 349-361.
  • Q. H. Ansari, Nonlinear analysis: Approximation theory, optimization and applications, Springer, New Delhi Heidelberg New York Dordrecht London,...
  • J. Banas, M. Jleli, M. Mursaleen, B. Samet, and C. Vetro, Advances in nonlinear analysis via the concept of measure of noncompactness, Springer,...
  • A. Berdellima, Compact sets and the closure of their convex hulls in cat (0) spaces, arXiv:2109.06002.
  • Bhupeshwar, D. K. Patel, M. Gabeleh, and M. E. Samei, On existence of solutions for $Psi$-Hilfer type fractional BVP of generalized higher...
  • A. Boutiara, M. M. Matar, Jehad Alzabut, M. E. Samei, and Hasib Khan, Investigation of ABC coupled Langevin fractional differential equations...
  • H. Busemann, Geometry of geodesics, Academic Press, New York, 1955.
  • A. A. Eldred, W. A. Kirk, and P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Mathematica 171 (2005),...
  • R. Espinola and A. Nicolae, Mutually nearest and farthest points of sets and the Drop Theorem in geodesic spaces, Monatshefte fur Mathematik...
  • A. Fernandez-Leon and A. Nicolae, Best proximity pair results for relatively nonexpansive mappings in geodesic spaces, Numerical Functional...
  • M. Gabeleh and H. P. A. Kunzi, Condensing operators of integral type in Busemann reflexive convex spaces, Bulletin of the Malaysian Mathematical...
  • M. Gabeleh, E. Malkowsky, M. Mursaleen, and V. Rakocevic, A new survey of measures of noncompactness and their applications, Axioms 11 (2022),...
  • M. Gabeleh and J. Markin, Optimum solutions for a system of differential equations via measure of noncompactness, Indagationes Mathematicae...
  • M. Gabeleh, D. K. Patel, and P. R. Patle, Darbo type best proximity point (pair) results using measure of noncompactness with application,...
  • M. Gabeleh and P. R. Patle, Best proximity point (pair) results via MNC in Busemann convex metric spaces, Applied General Topology 23, no....
  • M. Gabeleh and C. Vetro, A new extension of Darbo's fixed point theorem using relatively Meir-Keeler condensing operators, Bulletin of...
  • M. Jleli and B. Samet, Best proximity points for alpha-psi-proximal contractive type mappings and applications, Bulletin des Sciences Mathematiques...
  • P. R. Patle, M. Gabeleh, and V. Rakocevic, Sadovskii type best proximity point (pair) theorems with an application to fractional differential...
  • P. R. Patle, M. Gabeleh, V. Rakocevic, and M. E. Samei, New best proximity point (pair) theorems via MNC and application to the existence...
  • U. H. Rehman, D. Gopal, and P. Kumam, Generalizations of Darbo's fixed point theorem for new condensing operators with application to...
  • H. R. Sahebi, Manouchehr Kazemi, M. E. Samei, and Hasib Khan, Some existence results for a nonlinear q-integral equations via M.N.C and fixed...
  • B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for alpha-psi-contractive type mappings, Nonlinear analysis: theory, methods and applications...
  • A. Sultana and V. Vetrivel, Best proximity points of contractive mappings on a metric space with a graph and applications, Applied General...
  • S. T. M. Thabet, M. M. Matar, M. A. Salman, Miguel Samei, and M. E. Vivas-Cortez, On coupled snap system with integral boundary conditions...