Solvability of a Cayley Inclusion Involving $H$-Monotone in Banach Spaces

Abstract

In this paper, a new class of $H$-monotone in Banach spaces is considered and studied. The resolvent operator and Cayley approximation operator associated with the $H$-monotone are defined, and the Lipschitz continuity of Cayley approximation operator is also established. An application involves the solvability of a class of generalized Cayley inclusions with $H$-monotone in Banach spaces. By utilizing the technique of resolvent, an iterative algorithm is developed for solving such a class of generalized Cayley inclusions in Banach spaces. The convergence of the iterative sequence generated by the algorithm is proven under certain suitable conditions. The results are justified by means of a numerical example analytically and graphically using Python(matplotlib).

Key words: $H$-Monotone; Resolvent technique; Iterative algorithm; Cayley inclusion; Convergence.

Full Text

Article Information

Title	Solvability of a Cayley Inclusion Involving $H$-Monotone in Banach Spaces
Source	Methods Funct. Anal. Topology, Vol. 32 (2026), no. 1, 74-83
DOI	10.31392/MFAT-npu26_1.2026.08
Milestones	Received 12/06/2025; Revised 02/01/2026
Copyright	The Author(s) 2026 (CC BY-SA)

Authors Information

Khalid Fayaz
Department of Mathematics, University of Kashmir South campus-Anantnag, India

Mohd Iqbal Bhat
Department of Mathematics, University of Kashmir South campus-Anantnag, India

Hilal Ahmad Khanday
Department of Computer Sciences, University of Kashmir South campus-Anantnag, India

Mudasir A. Malik
Department of School Education J&K Govt. Kashmir, India

Citation Example

Khalid Fayaz, Mohd Iqbal Bhat, Hilal Ahmad Khanday, and Mudasir A. Malik, Solvability of a Cayley Inclusion Involving $H$-Monotone in Banach Spaces, Methods Funct. Anal. Topology 32 (2026), no. 1, 74-83.

BibTex

@article {MFAT2213,
    AUTHOR = {Khalid Fayaz and Mohd Iqbal Bhat and Hilal Ahmad Khanday and Mudasir A. Malik},
     TITLE = {Solvability of  a Cayley Inclusion Involving $H$-Monotone    in Banach Spaces},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {32},
      YEAR = {2026},
    NUMBER = {1},
     PAGES = {74-83},
      ISSN = {1029-3531},
       DOI = {10.31392/MFAT-npu26_1.2026.08},
       URL = {https://mfat.imath.kiev.ua/article/?id=2213},
}

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