Some aspects of generalized Dunkl-Williams constant in Banach spaces

This article delves into an exploration of two innovative constants, namely DW(X,{\alpha},\b{eta}) and DWB (X,{\alpha},\b{eta}), both of which constitute extensions of the Dunkl-Williams constant. We derive both the upper and lower bounds for these two constants and establish two equivalent relations between them. Moreover, we elucidate the relationships between these constants and several well-known constants. Additionally, we have refined the value of the DWB (X,{\alpha},\b{eta}) constant in certain specific Banach spaces.