QUASI-AVERAGED AND QUASI-DOUBLE AVERAGED MAPPINGS
Applicable Nonlinear Analysis, Volume 2, Issue 2, August 2025, Pages: 122–145
HIMANSHU BARANWAL
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India
A. K. B. CHAND
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India
ADRIAN PETRUȘEL
Faculty of Mathematics and Computer Science, Babeș-Bolyai University Cluj-Napoca, Romania
JEN-CHIH YAO
Center for General Education, China Medical University, Taichung, Taiwan
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan
Abstract
We introduce the concept of quasi-averaged mappings within quasi-normed linear spaces. Employing these class of mappings, we derive fixed point theorems and demonstrate convergence results for the Krasnoselskij iteration method associated to various types of enriched contractions. This comprehensive analysis encompasses a range of contraction types, such as Chatterjea, Kannan, Bianchini, Ćirić, Hardy-Rogers contractions, and enriched almost contractions in quasi-Banach spaces. In addition, we present the definition of three distinct types of quasi-double averaged mappings associated with weakly enriched contraction mappings. Moreover, we emphasize the presence of fixed points within these mappings, underlining both their existence and uniqueness. Some illustrative examples are furnished to support our theoretical results and effectual generalization. Finally, we present sufficient conditions guaranteeing the equivalence between the set of fixed points of the quasi-double averaged mapping associated with a weakly enriched mapping and that of the weakly enriched contraction mapping itself.
Cite this Article as
Himanshu Baranwal, A. K. B. Chand, Adrian petrușel, Jen-Chih Yao, Quasi-averaged and quasi-double averaged mappings, Applicable Nonlinear Analysis, 2(2), 122–145, 2025