Shadows and gravitational weak lensing by the Schwarzschild black hole in the string cloud background with quintessential field*

In this work, we observe that in the presence of string cloud parameter $a$ and quintessence $\gamma$, with equation state $\omega_q={-2}/{3}$ radius shadow Schwarzschild black hole increases as compared pure case. The existence both quintessential dark energy strings magnify size hence strength gravitational field around increases. Using data collected by Event Horizon Telescope (EHT) collaboration for M87* Sgr A*, obtain upper bounds on values parameters $\gamma$. Further, see effects $\gamma$ rate emission hole. We notice is higher clouds quintessence. Moreover, study weak deflection angle using Gauss-Bonnet theorem. show influence angle. increase $\alpha$.