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The purpose of this paper is to combine and extend some recent fixed point results of Suzuki, T., [A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317] and Secelean, N. A. & Wardowski, D., [ψF-contractions: not necessarily nonexpansive Picard operators, Results Math., 70 (2016), 415-431]. The continuity and the completeness conditions are replaced by orbitally continuity and orbitally completeness respectively. It is given an illustrative example of a Picard operator on a non complete metric space which is neither nonexpansive nor expansive and has a unique continuity point. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend the result of Wardowski (Fixed Point Theory Appl 2012:94, 2012) by introducing a new class of Picard operators which strictly includes the family of F-contractions. For such operators some fixed point theorems are proved. It is showed that there exist Picard self-mappings on a complete metric space that are neither nonexpansive nor expansive. [ABSTRACT FROM AUTHOR]

This article deals with linear operators Ion a complex Hilbert space H, which are bounded with respect to the seminorm induced by a positive operator A on H. The A-adjoint and A1/2-adjoint of T are considered to obtain some ergodic conditions for T with respect to A. These operators are also employed to investigate the class of orthogonally mean ergodic operators as well as that of, A-power bounded operators. Some classes of orthogonally mean ergodic or A-ergodic operators, which come from the theory of generalized Toeplitz operators are considered. In particular, we give an example of an A-ergodic operator (with an injective A) which is not Cesáro ergodic, such that T* is not a quasiaffine transform of an orthogonally mean ergodic operator. [ABSTRACT FROM AUTHOR]