Abstract: FIXED POINT THEOREMS FOR φ-NONEXPANSIVE SEQUENCES IN BANACH SPACES Behzad Djafari Rouhani Department of Mathematical Sciences, University of Texas at El Paso, 500 W. University Ave., El Paso, TX 79968, USA Email: behzad@utep.edu Abstract. Let X be a real Banach space with norm | · |. A sequence {xn} in X is called a nonexpansive sequence if |xi+1 − xj+1| ≤ |xi − xj |, ∀i, j ≥ 1. When X is a real Hilbert space H, ergodic theorems for such sequences were proved by Djafari Rouhani in 1981, and it was stated as an open problem whether those results could be extended to Banach spaces. By introducing the notion of φ-nonexpansive sequences and mappings in X, we give a partial affirmative answer to this open question. AMS Classification Number: Primary 47H25; 47H09; 47H10; 47J25. Secondary 37A30; 47H20; 47H30; 47H05.

Biography: Behzad Djafari Rouhani received his PhD degree from Yale University in 1981 under the direction of the late Professor Shizuo Kakutani. He has more than 40 years of academic experience in many universities around the world. He is currently a Professor of Mathematics at the University of Texas at El Paso in USA. His interest is in the field of Nonlinear Functional Analysis, more specifically, Nonlinear ergodic theory, nonlinear evolution and difference equations, fixed point theory, variational inequalities and optimization. He has published more than 70 research papers in peer reviewed journals of his field.