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In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

In this paper, we present a explicit viscosity technique of nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorem of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this paper extend and improve some recent announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

In this paper, we present a explicit viscosity technique of nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorem of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this paper extend and improve some recent announced in the current literature. [ABSTRACT FROM AUTHOR]

The aim of this report is to study modulus of convexity δB of a quasi-Banach space B. We prove that δB is convex, continuous, nondecreasing and for arbitrary uniformly convex quasi-Banach space B, δB ... We also prove that a quasi-Banach space B is uniformly convex if and only if δB(∈) ≥ 0. Moreover we prove that a non-trivial quasi-Banach space B is uniformly non-square if and only if δB(∈) > 0. [ABSTRACT FROM AUTHOR]

The aim of this report is to study modulus of convexity δB of a quasi-Banach space B. We prove that δB is convex, continuous, nondecreasing and for arbitrary uniformly convex quasi-Banach space B, δB(∊) = 1 - 1/C√1 - ∊2C2/4 . We also prove that a quasi-Banach space B is uniformly convex if and only if δB(∊) ≥ 0. Moreover we prove that a non-trivial quasi-Banach space B is uniformly non-square if and only if δB(∊) > 0. [ABSTRACT FROM AUTHOR]

In the present note we will introduce a Binomial distribution series and obtain necessary and sufficient conditions for this series belonging to the classes T(λ, α) and C(λ, α). An integral operator related to this series is also considered. [ABSTRACT FROM AUTHOR]

The generalized von Neumann-Jordan constant C(p)NJ (B) and the James constant J(B) for a quasi-Banach space were introduced in [7]. In this note, it is shown that C(p)NJ (B) ≥ 2 for any quasi-Banach space B andC(p)NJ (B) < 2 if and only if B is uniformly non-square. Along with relationship between J(B) and C(p)NJ (B), the criterion for the uniformily smooth quasi-Banach space is also established. [ABSTRACT FROM AUTHOR]