Document Type : Research Paper

Authors

• Adesanmi Mogbademu ¹
• Jong Kyu Kim ²

¹ Research Group in Mathematics and Applications, Department of Mathematics, University of Lagos, Lagos, Nigeria

² Department of Mathematics Educations, Kyungam University, Masan, Kyungnam, Republic of Korea, Korea

Abstract

In this paper, we prove strong convergence results for a modified Mann iterative process for a new class of I- nearly weak uniformly L-Lipschitzian mappings in a real Banach space. The class of I-nearly weak uniformly L-Lipschitzian mappings is an interesting generalization of the class of nearly weak uniformly L-Lipschitzian mappings which inturn is a generalization of the class of nearly uniformly L-Lipschitzian mappings which inturn generalises uniformly L-Lipschitzian mappings. Our theorems include some very recent results in fixed point theory and applications, in the context of nearly uniformly L-Lipschitzian mappings.

Keywords

• Modified Mann iteration process
• Banach space
• Fixed point
• I-nearly weak uniformly L-Lipschitzian