A Generalization of C´ iric´ Fixed Point Theorems

Poom Kumama, Nguyen Van Dungb, Kanokwan Sitthithakerngkiet;c,d
aDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang
Mod, Thung Khru, Bangkok 10140, Thailand
bInstitute of Research and Development, Duy Tan University, R.809, K7/25 Quang Trung, Da Nang, Viet Nam
cNonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of North
Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand
dFaculty of Mathematics and Information Technology Teacher Education, Dong Thap University, Cao Lanh City, Dong Thap Province, Viet Nam

In this paper, we state and prove a generalization of C´ iric´ fixed point theorems in metric space by using
a new generalized quasi-contractive map. These theorems extend other well known fundamental metrical
fixed point theorems in the literature (Banach [1], Kannan [11], Nadler [13], Reich [15], etc.) Moreover, a
multi-valued version for generalized quasi-contraction is also established.



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